Topics of Applied Mathematics II

Code:

M404

Acronym:

M404

Instance: 2010/2011 - 2S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=2633
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master's degree in Mathematics for School Teachers

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:MPRO	13	PEOficial Mestrado Matemática Professores	1	-	7,5	-

Teaching language

Portuguese

Objectives

To bring up to date knowledge and to supply new perspectives in branches of the mathematics with links to other domains, facilitating the desirable thematic transversality on middle and secondary school teaching.

Program

1. Numerical Analysis
Errors, absolute and relative errors. Number of correct decimal places and of significant digits. Rounding rules. Computer representation of floating point numbers. Rounding errors and truncation errors.
Solution of nonlinear equations by iterative methods. Bisection method. Newton method and variants.
Solution of algebraic equations. Locatization and numerical computation of the roots of a polynomial.

2. Discrete Mathematical Modeling
One-dimensional models: exact model for change; resolution of linear and affine dynamical system.
Two-dimensional models: equilibria and their stability for the corresponding dynamical system.
Modeling with proportionality.
Fitting a model to data: the graphical method and the least square method.
Experimental modeling.

Mandatory literature

Heitor Pina; Métodos Numéricos, McGraw-Hill, 1995. ISBN: 972-8298-04-8
Claude Brezinski, Michela Redivo Zaglia ; Méthodes numériques itératives, Elipses, 2006. ISBN: 978-2-7298-2887-5
000102121. ISBN: 978-0-495-55877-4

Complementary Bibliography

José Alberto Rodrigues; Métodos numéricos : introdução, aplicação e programação, Sílabo, 2003. ISBN: ISBN 972-618-311-1

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	75,00
	Total:	-	0,00

Calculation formula of final grade

Each module will have its own assessment method and will follow the proportion:
Numerical Analysis: 10/20
Discrete Mathematical Modeling: 10/20

The final mark will be the sum of the marks obtained in the two modules.